OFFSET
0,8
COMMENTS
LINKS
Michael De Vlieger, Table of n, a(n) for n = 0..11475 (rows n = 0..150, flattened)
FORMULA
T(n, m) = 0 if n<m; T(0, 0)=1, T(n, 0)=0 if n >= 1; T(n, m) = T(n-1, m)+sum(T(k, m-1), k=m-1..n-1) if n+m even and T(n, m) = T(n-1, m)+sum(T(k, m-1), k=m-1..n-1)-binomial((n+m-3)/2, m-1) if n+m odd, n >= m >= 1.
EXAMPLE
Triangle begins:
{1};
{0,1};
{0,1,1};
{0,2,2,1};
...
Pe(4,x^2)=1+6*x^2+x^4.
MATHEMATICA
t[n_?EvenQ, k_?OddQ] := Binomial[n, k]/2; t[n_, k_] := (Binomial[n, k] + Binomial[Quotient[n, 2], Quotient[k, 2]])/2; Flatten[Table[t[n - 1 + m, n - m], {n, 0, 12}, {m, 0, n}]] (* Michael De Vlieger, Sep 28 2024, after Jean-François Alcover at A034851 *)
CROSSREFS
KEYWORD
AUTHOR
Wolfdieter Lang, Jun 19 2001
EXTENSIONS
More terms from Michael De Vlieger, Sep 28 2024
STATUS
approved